Asked by Niles Martinsen
on 11 Sep 2012

Hi

I have a relatively simple set of coupled ODE's that I am trying to solve by ODE45. The following is the content of the .m-file, which shows the coupled system:

function xprime = eoms(t, x)

xprime = [ 1e9 + 5.0e4*x(3) - 50*x(1); 4.0e1*x(1) - 3.3e3*x(2); 2.0e3*x(2) - 5e4*x(3) + 3.5e7*heaviside(t-1)*x(4); 1.0e3*x(2) - heaviside(t-1)*5.0e7*x(4)];

I solve it using the following command:

x0 = [0 0 0 0]; tspan = [0, 2]; [t, x] = ode45(@eoms, tspan, x0);

However when I compile MatLAB just keeps calculating, it doesn't give me a result. I think it has something to due with the fact that the Heaviside step-function, because if I take it out then it nicely solves the remaining part. I have also tried in a competing software, and the same thing happens (actually, there the solver just gives an error).

Maybe it is also due to the very rapid rates in the equations. Anyhow, I am really lost on what to do - unfortunately I need the transient behavior, so I can't just assume steady-state for some of the equations.

Do I have any options here?

Thanks in advance.

Best, Niles.

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Answer by Star Strider
on 11 Sep 2012

Edited by Star Strider
on 11 Sep 2012

Accepted answer

You have a ‘stiff’ system, and `ode45` is not the best option for it, although it's an appropriate initial experiment. If `ode45` seems not to work (and the system otherwise seems to be solvable in some situations as yours was), switching to `ode15s` is appropriate, especially in systems with coefficients of widely-ranging magniudes such as yours are (from 4E+1 to 1E+9).

After experiencing the same problem you did with `ode45`, I ran your code with `ode15s` and it solved your `eoms` system in 1.2225 seconds.

So I suggest you simply change your ODE function call to:

[t, x] = ode15s(@eoms, tspan, x0);

and enjoy the results!

Also, I coded your function as an implicit function to run it, avoiding the need to save a separate function `m-file`. (This isn't always possible, but it works in many situations.)

The function:

eoms = @(t,x) [1e9 + 5.0e4*x(3) - 50*x(1); 4.0e1*x(1) - 3.3e3*x(2); 2.0e3*x(2) - 5e4*x(3) + 3.5e7*heaviside(t-1)*x(4); 1.0e3*x(2) - heaviside(t-1)*5.0e7*x(4)];

and the call to it changes to:

[t, x] = ode15s(eoms, tspan, x0);

Niles Martinsen
on 13 Sep 2012

Thanks, that is very kind of you.

Star Strider
on 13 Sep 2012

As always, it is my pleasure to help!

Answer by Shashank
on 28 Jun 2013

Star Strider, could you please help me solve this set of four coupled ODEs?

tpcl = @(xi,y) [y(2); ((1 + (y(2)*y(2)))^(1.5))*(y(3) - (A/(y(1)^3)))/sigma; -3*mu_l*y(4)/(rho_l*h_lv*(y(1)^3)); (Twall - Tsat - (Tsat*y(3)/(rho_l*h_lv)))/((y(1)/k_l) + R_int)];

xi_step = 0:1e-8:xi_end;

[XI,Y] = ode15s(tpcl,xi_step,[delta_ad deltaprime_ad delta_p_ad Q_ad]);

Here, apart from the variables y(1), y(2), y(3) and y(4), everything is a constant. I tried ode45 and ode15 but it still did not work. The results look unrealistic to say the least.

Marc
on 29 Jun 2013

You need to give us your constants. You may want to post this in the newsgroup, which is more for helping folks with there code snafus.

Answer by MUFTAH AKROUSH
on 16 Dec 2015

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## 1 Comment

## MUFTAH AKROUSH (view profile)

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/47851#comment_329978

Hi. I want to know How i can solve 4 differential equations like this v_dot(1)= 3*x(1)+v(2)-x(2)+v(3)-x(4)-x(5)+v(4); with 2 variables with Function command and ode45?